Last week I started this short series of articles on making your own props for photoshoots. This mini-series was built on simple techniques using materials you can buy from your local crafts, hardware or car maintenance store. The techniques and materials I will discuss today are not scary and are hugely robust – the same techniques I will outline are used in car body repair, for the repair of walls, window frames and cracked pipes and it is commonly used to skin high performance model helicopters and planes, and even real ocean going yachts and fishing boats – all with materials you can buy in your high street and work on in your garden without massive tool collections. Fibreglass is also used in medical applications such as casts for setting broken bones, however this is using medical grade safety resins which are not available in stores – the actual glass fibre material is the same though.
The prop design process was broken into 4 sections:
- pepakura – building the skeleton of your prop
- resin and fibreglass (this article)
- body filling and sanding (a.k.a. bondoing)
This week I talk about reinforcing your pepakura props with polymer resins, and how to massively strengthen your props using fibreglass. I will demonstrate this in two separate steps, even though fibreglassing uses resin. You can reinforce many things with resin and fibreglass, not just paper (from pepakura), so if you are wanting to repair that hole in your shed roof, then this will work for you just the same.
The story so far…
So you’ve decided on a prop that you want for your shoot, or item you want in your house / office, and you have made it using pepakura by following the previous article. We are going to Fibreglass it to make it a lot stronger, but we can’t apply fibreglass directly to your paper model – its not strong enough to support the weight. Not to worry, first we will give your model a good coat of polymer resin to make it tough enough to apply the fibreglass.
At the end of this article, if you have followed the process, your model will be pretty sturdy but surprisingly light for the strength – it may even be load bearing. The prop will need body filling/building using filler materials (discussed next article) in order to get proper shaping and fine details in it.
OK so before we even begin, lets talk safety…
We’re going to be talking resins, fibreglass, catalysts and hardeners. These are harmful materials, but when handled properly we will minimise risks, manage hazards, and also get a more professional finish.
Working with polymer resins and fibreglass have different associated hazards (resins being more chemical, and fibreglass being more physical in nature) and to cover both you WILL need the following. I don’t care if you have been working with this stuff for years, or you live in the US where safety apparently doesn’t matter – do it right and be safe, so that you can do it right for many years to come.
You WILL need:
- Eye protection. I use BS-EN/ISO certified lab specs (I’m a chemist, its part of my normal work attire). You can get full goggles for a couple of pounds from B&Q, or even Wilkinsons. Don’t scrimp – glass fibre dust, or a splash of epoxy resin in your eye is not pleasant, with potentially long term adverse effects.
- Gloves – Latex or nitrile are tailored to give the best fit. Those really cheap sandwich bag type gloves are never a good fit in my opinion. Again, B&Q, Wilkinsons or even the local pound shop have them. They are disposable so ensure you have a bunch for when you spill on them, as you will want to change them frequently. When working with glass fibre, I suggest using good old kitchen gloves as well, as the glass fibre can pierce nitrile and latex gloves.
- Respirator. If you are working indoors, get a respirator. If you are working outdoors, get a respirator. If you are working in outer space on an asteroid, get a space suit – and a respirator. Dust masks won’t cut it. You’ll need at least a half mask respirator, preferably with an A2/P2 filter set (for chemical and particulate hazards). You can pick up a 28 day disposable one from B&Q for about £15. I recommend getting a decent 3M one – they have replaceable filters and are really comfortable compared with others I have worn in the lab. Read the instructions and know how to take care of it – I wear one of these with A2+P2 filters – Having worked with large amounts of cyanide and other chemical nasties for extended periods with the same model in the past.
- Working in a well ventilated area. Ideally outside, but a garage with the door open or ventilated basement will be fine. Try and ensure that your work area will not be disturbed for a day or two (e.g. to let your props cure fully).
- Long sleeved tops and trousers. Glass fibres are irritants, and the chemicals we are working with can cause burns. Be sensible – don’t do this in shorts and sandals. If you want to feel totally protected, you can buy a cheap labcoat, cover-alls or even a disposable dust suit (for £1 at some pound shops!).
ALWAYS read the labels on any materials you are working with – get the material data safety sheet (MSDS) from the supplier. Over protect rather than under protect. Monomer resins often contain additives that can cause issues such as respiratory or neural damage.
OK that sounds all a bit serious but realistically mechanics, boat builders, and handymen have been working with these materials for decades. Just be on the safe side, wear the proper kit, and respect the materials you are working with.
If you watch youtube videos on how to make models with fibreglass you will get a whole range of people with varying opinions and practices with regards to personal safety – use your own fair judgement and remember: you cannot be too safe.
I hereby absolve myself of any responsibility for your well being regarding this (or any other) project.
What is “Resining” and why would I want to do it?
Before, I discussed making props out of cardstock using pepakura. If you have joined me from reading that article you will have a nicely built paper prop. Congrats on sticking with it and realising your 3D design. Your paper prop is a bit stronger than you probably thought, with all the curves, folds and glue, but realistically you can’t use it in an actual shoot as it is still far too weak.
Coating your prop in a polymer coat will go some way to making it stronger -more than that: polymer resins are compatible with a far larger array of spray paints and finishes that a paper model are not. This will be necessary for getting the finish that you want. When a pepakura model has been suitably coated / impregnated with resin, we will be looking to properly strengthen it, and for this we can use a vast array of reinforcing composite materials. Later in this article I will discuss working with fibreglass, but for the most part many composite reinforcing materials are prepared and treated the same way.
What is Polymer Resin
This is tricky to answer for me to give without getting too technical – I have a PhD in chemistry and will get carried away. I will attempt to keep this nice and simple….
A polymer is a material made up of repeating chemical units (“monomers”) joined end to end. We use them all the time – polyester is a polymer of “ester” subunits repeated over and over to make threads or sheets. Teflon is a polymer (its proper name is PTFE – poly tetrafluoroethyelene), superglue is a polymer too, as are epoxy glues. You will notice something about the last two examples: we use them as liquids and then over time they set (or “cure“) to become hard. This is very important for our application.
Most polymers are made from having a liquid form of the monomer (the single unit that repeats in the polymer), and then a “catalyst” that makes the monomers react with eachother to build chains or matrices of these repeating monomers (hence making a polymer). If the part of the “catalyst” components is incorporated into the final polymer, then it is not strictly a catalyst, but a hardener.
A geeky aside: DNA is a technically biological polymer. It uses an enzyme called DNA polymerase as its “catalyst”.
Common Polymers to prop build with
For the thousands of polymers out there to work with there are realistically two classes of readily available polymer resin to build with: Epoxy, and Polyester. They are basically treated the same way but there are little nuances in their use so I’ll quickly talk you through each.
Polyester resin is very commonly used in car repair, and you can buy it in the UK from Halfords. David’s FastGlas is the stuff, and its pretty cheap (under a tenner for half a litre of resin and enough catalyst to cure it). This is a free radical initiated polymer, using a true catalyst (benzoyl peroxide, BPO); usually as a few drops of BPO to 20 ml of resin. Typically for polyesters, you need 1-2 % catalyst by weight, FlastGlas uses much more in order to cure really fast – ALWAYS read the label for proper ratios. FastGlas will give you about 5-7 min pot life (the time which you can easily work with it as a liquid) at 20 Celsius (and more if its a bit colder). It boasts being fully cured and ready to sand within 20 min at 25 Celsius, but to be honest its more like 45-60 minutes in my experience ( 18-20 Celsius)
Polyester resins tend to smell (read: reek), and the smell often doesn’t quite disappear for anything up to a few days. If you put a layer on and leave it in the wind or strong sunlight, you can deactivate the polymerisation reaction (UV light and oxygen terminate the cascade) – meaning when you have worked with it, leave it somewhere out of air flow, and in the shade – ideally under an upturned box or the surface wont ever fully cure – you can sand off the tacky layer (which also reduces the smell significantly) if it doesn’t go hard after a day – it’ll gum up your sand paper so use some cheap stuff. As its a true catalyst – you can vary the amount you add to slow or speed up the reaction – using more catalyst than needed is called ” mixing a hot batch” as it gets hot to the touch. Polyester resins contain harmful materials such as styrene and the catalyst is dangerous to the skin. But once cured, polyester completely safe – we use polyester to make clothing and even food packaging.
Epoxy resins have been used as adhesives for decades. It is more difficult to find decent epoxy resin sources in the high street; a model shop might sell it, but if not my favourite source online is Easy Composites -It’s rare that I endorse anything publicly but these guys are cost effective and are always helpful. The main reason why you would want epoxy resins is that they don’t smell (they are virtually odourless in comparison to epoxy resins). They are still harmful until cured though – and the amine hardener can cause burns if it gets on your skin. Another great reason for using epoxies are that they cure colourless. The hardener component is not catalytic, but becomes part of the polymer – so normally you use a lot more of the hardener than you would a catalyst with poly ester resins (you buy a kit that has the proper ratio of resin to hardener – often as high as 3:1 by weight respectively. Again, always read the label for your batch to ensure proper ratios). As the hardener becomes part of the polymer, you sometimes have a choice as to which hardener you want – some cure fast (10-15 min pot life, full cure in 4-8 hours and some cure slow (45 min pot life, 16 hour to full cure). Slow cure epoxies tend to have a bit more strength, but for our purposes fast cure is just fine. Epoxy resins tend to be a little more expensive than polyester resins, but I think the lack of odour alone is worth it (about 500 ml kit for £10 but can be more).
If you are buying from easy composites, You’ll want EL2 epoxy, the fast curing kit.
OK, so that’s all you need to know about polymer resins for this bit. Lets look at what you’ll need:
So from left to right:
- Something to protect your surfaces – like a dust sheet. I often just use old cardboard boxes instead, as dust sheets ooutdoors can get blustery.
- Some cheap, DISPOSABLE brushes. These were 5 for £1 from the poundshop.
- Resin and hardener/catalyst – here I have shown polyester resin (FastGlas), and catalyst (U-POL BPO)
- A measuring cup – this is a 50 mL cup for medicines, you can use anything disposable
- A small Mixing bowl and spoon / mixing stick – another pound shop special (£1 for 4 ice cream pots and spoons). You can even use paper cups, but I fear they might get a bit flimsy when the resin is in there.
- If you are working with epoxy resins, you will need a kitchen scale too – or something to weigh out your materials.
OK enough background. We have the safety kit, we have our resin and our pepakura / prop / other item that we wish to resin, and we have a workspace. Let’s get our polymerisation on.
Step 1: Prepare your work space.
Clean, clutter free and clear of people, you need to feel secure so you dont make any rushed mistakes. Outdoors is best or at least a garage with the shutter fully open for air flow.
You will need something to sit your prop on when its coated – a cardboard box lid is perfect. Have a rubbish bag / carrier bag ready to throw old gloves, brushes and packaging into ready and held open for you – throwing refuse away as you go makes clean up as easy as picking up the bag.
Step 2: Get kitted up.
Gloves, respirator and safety specs on. They will stay on for the duration. Have spare gloves within easy reach. Have some absorbent material (read: kitchen roll) ready in case of any spillages, but realistically there should be zero spillage: the resins are viscous enough that you wont splash them.
Step 3: Prepare your model.
Ensure your model is clean and free of dust, and any glue is fully set – a quick brush down with a clean brush will ensure this.
Step 4: mix up your resins
Carefully measure out the resin by volume or weight depending on whether it’s polyester or epoxy. If doing this by weight, you can do it directly into your mixing pot. Start with about 30 g of epoxy resin ( meaning 40 g total including hardener), or 40 g of polyester. This will be enough to generously coat a life size helmet prop inside and out. Work in small batches and make up more if you need more rather than making huge amounts and it going off in your pot before you’ve had a chance to use it – especially if you are working with Fastglas as it becomes unworkable faster than epoxies.
Once you add the harderner component the clock starts but DO NOT PANIC. 10 minutes is plenty of time to work your resin into your prop.
MIX IT THOROUGHLY – for at least a full minute with a stick / stirrer. A poorly mixed resin will not cure evenly or maybe not even at all.
Step 5: Apply your resin
Use one of your disposable brushes and take a generous amount of resin and apply to your model. Don’t worry about being neat – just get it on. Coat the outside. If you are worried about neatness, you can coat the outside and let it fully cure before coating the inside. Or if you have used decent cardstock (200 gsm +) you can coat the inside and outside in one run – you will get resin on your gloves this way, but its OK – just change the gloves when you are done.
Step 6: Leave to cure
Your model has now been painted in resin will be sticky for a while depending on the resin you used, how thick your coat is, and the temperature. Ensure that it can cure undisturbed in the warm. Keep your model out of the wind, and as dust free as possible – grit and dust can end up lodged in your resin and set – it’s not a problem as you can sand it out and eventually it will be covered in body filler, but it will annoy you. As aforementioned, an upturned box is ideal, or if your prop is large, allow it to cure in a shed or under your garden table with a dust sheet over the table to make a tent. With epoxy resins you can cure it in full sunlight just fine. To put a sense of scale to it: on a fine British Spring/Summer’s day (20 Celsius), Fastglas took about 40 min to cure to a non-tacky surface, whilst EL2 fast curing epoxy took 6 hours. Fastglas had a slight smell of polyester until sanded quickly, the epoxy was odourless when cured. Either way, you are best off leaving them over night before moving on with the next stages.
Notes from the field:
1. Working in small batches reduces resin waste, makes for better mixes and makes any hazards more manageable (e.g. spills). If you didn’t work fast enough, and your resin starts to cure in your mixing tub, simply put it aside and make up a new batch – never top up a batch that is already curing. Small batches stop this happening – always aim to have just enough to do what you want to do and not more.
2. Resin will soak into the paper of your prop making it a bit translucent. This makes it effectively a paper-resin composite. If you used thin cardstock (say 150 gsm), then your model might be prone to warping when wet – you might need to support it whilst it cures, or coat it inside first, allow it to cure, and then coat the outside, to reduce the load on the paper.
3. A cured prop is stronger, but still flexible, don’t stress it too much – a resined prop will not tear like paper, but will snap / crack instead.
4. Sharp edges which were paper are now sharp plastic, be careful not to get spiked / cut on any protruding or sharp edges of your prop.
OK that’s it. You should have a toughened resin coated prop. It is a lot stronger than the paper but isn’t much thicker and is still very light weight – but its not really strong enough to wear if it’s armour, helmet or prop weapon. To make it studio-tough we are going to fibreglass it. The resin coat was really to ensure that its strong enough to fibreglass – the paper model would not be strong enough to support the weight of the fibreglass, nor would it keep its shape when you push and drag your fibre glass sheets into place.
Fibreglass and What it can do
Fibreglass is also called Glass Reinforced Plastic (GRP). It is a high performance composite material comprised of a matrix of wetting resin polymer (the same resin used above) and glass fibre sheet, tissue or mat. Composite materials like this exist all over the place, from motorcycle helmets to boats, to aircraft and even buildings, and there are a range of materials you can use as the reinforcement.
In most cases a composite construction material is just a solid reinforcement material that is soaked (“impregnated”) with a resin that cures hard – it gives better bend, compression and tensile strength than the sum of the components.
Common reinforcement materials include glass fibre, aramid (Kevlar) and carbon fibre. You have no doubt already worked with a simple composite as a child: paper reinforcement impregnated with PVA or water/flour matrix, a.k.a. Papier-mâché. You can see a recent Papier-mâché Venetian mask build here
Some model makers use use cotton and PVA – which is a bit heavy, but surprisingly strong, and pretty much non toxic.
So why glass? Well glass can be extruded, woven and easily cut, it is also very light weight – GRP is often stronger than its weight in steel for certain loads.
The good news is that GRP is so commonly used in car body panel repairs, you can buy it from Halfords and other auto repair stores. You can even buy it from some craft stores. If you are going to buy it from Halfords, you can buy a FastGlas kit, which includes fibre mat or tissue, resin and hardener, mixing cup, gloves, mixing sticks and brush. The small kit is about £8, and the larger one is about £12.
Mat, Woven Sheet or Tissue
Glass fibre is available as a fibre mat, a woven sheet, or as “glass tissue”. Each have their own benefits:
Chopped Glass Mat
Fibre mat is a thick (2 mm or so) sheet material with chopped glass fibres at various directions and angles stuck together with a powder binder. It is pretty cheap, and you can get it from Halfords. Structurally it is strong when impregnated with resin and can really soak it up. It is a bit of a nightmare to cut properly though, as the strands are in random directions. I tend to cut with a pair of sharpened scissors, and drag and tear it out a bit, which makes the edges of the pieces frayed and random – which is great for covering irregular edges.
Woven Sheet Glass Fibre
This is the strongest glass fibre – it is a continuously woven material and can be bought by density (200 gsm – 400 gsm +) a couple of coats of 400 gsm is the kind of reinforcement used to skin a fishing boat hull – it is load bearing – a balloon coated in it will easily take a man’s body weight without a fuss. A single layer of 150-200 gsm is plenty strong for most applications, especially props. As the woven sheet is not random, cutting it is a bit easier, but you will need sharp scissors or shears. Woven sheet tends to be a little more expensive than glass mat, but not much at all.
Fibre tissue is a lightweight and very thin glass fibre sheet. It is much thinner than the mat, and does not absorb so much resin, and so is weaker than both mat and woven sheet. Fibre tissue is very easy to cut with scissors, and gives the finest finish, so some people prefer to use it as the final layer ontop of the rough mat or thick woven sheet if multi-layering. Fibre tissue is also used in car repair for those holes that need to be strong enough to not bend when pressed, but not required to be very strong. You can of course layer up the fibre tissue to make it as strong as mat or woven sheet, but it wont be cost effective. Fibre tissue is cheaper than woven sheet and fibre mat. You can buy this from Halfords.
As I said, costs can vary between types, but realistically the variance store to store often outweighs the cost difference between type. As an example, here are the costs per metre from my preferred supplier.
30 gsm glass surface tissue – £1.50 per square metre (Halfords: £3.49)
100 gsm woven twill sheet – £3.08 per square metre
200 gsm woven twill sheet – £3.26 per square metre
300 gsm woven twill sheet – £3.78 per square metre
300 gsm chopped mat sheet – £1.54 per square metre (Halfords: £4.49)
As a bit of guidance: for coating life sized full-face helmet, you’ll typically use less than a square metre of glass fibre.
When working with polymer resins, the hazards are mainly chemical in nature. Working with fibreglass offers more physical hazards – which are often overlooked.
Sharps – Irritant
Glass fibre on the skin (especially fine glass tissue) is an irritant, and you can get pricked on the strands. Always wear gloves when handling glass fibre – I often use rubber kitchen gloves when handling it, as glass wont get through so easily.
Dust – Respiratory Hazard
When working with fibreglass, you are likely to break some of the strands. You will also be cutting the fibres, and later you’ll be sanding and tidying up edges. This will generate glass dust. Glass dust is a real hazard – be sure to wear a respirator with a P2 particulate filter – a dust mask may not be good enough. You already have a respirator, so wear it. You my want to work outside, and hiding your skin from the glass is a good idea – wear long sleeved clothing, or better, coveralls. Goggles are a must.
You can also minimise risks here by using tools and processess that are unlikely to through up dust – where possible use toothed tool such as a coping saw rather than rotary cutters such as a Dremmel and a cutting disc, and you will minimise dust significantly- More on this later.
OK so lets get it done.
What you’ll need:
- Glass Fibre: Sheet, mat or tissue. How much you’ll need will depend on your project: 0.25 square metres is usually enough for a single coat for of a life sized helmet.
- Resin, mixing pot, brushes (same as the resin process above): The same kit as you used to resin coat your pepakura prop – you will need a lot more resin this time, as the glass fibre matrix will soak it up.e.g. The helmet prop shown in this thread, I used about 30 g of resin to coat inside and out. I used 100 g (as 2 x 50 g batches) of resin when fibreglassing a single layer of chopped fibre mat.
- Scissors to cut your glass fibre. Pre-cut your pieces before mixing up your resin.
Ready? Let’s go!
OK, so we are ready to go – we are going to make a layer of glass fibre and impregnate it with more resin. When its cured it’ll be really tough.
- If you are fibreglassing a prop that has fine detail, angles or edges, or you are making a helmet, body armour or the like, fibreglass the inside face of the prop – this will leave your external shape from the pepakura untouched, and easier to build on with filler. If you cannot fibreglass the inside (e.g. you’ve made a lamp stand, prop-weapon or something similar, use a thinner/finer glass fibre and be as neat as you can.
1. Set your workspace
Set it up as it was when you did you first resin coatings. Good air flow and a clean space makes for a safer job.
2. Get your safety kit on
Respirator, gloves and safety specs at a minimum. Make sure your respirator is comfortable – you don’t want to try and adjust it with resin or glass fibres on your fingers.
3. Pre-cut your glass fibre
Cut your fibre into small squares (e.g. 5 cm by 5 cm) which you will then lay into / onto the prop. If you are going for a super neat job you could even use a few drops of PVA or a very light coat of spray adhesive to hold the glass fibre in place until you resin it. You will be overlapping the edges of the glass fibre, so ensure you have enough to cover what you need, and then a bit more of smaller / shaped pieces to fit random bits that you missed.
4. Mix up your resin
As before in your resin coating step. You will need much more this time around, but work in small batches (say 50 g batches). The clock is now on.
5. Apply your glass fibre
If you have used spray adhesive or PVA to pre-position the fibre inside your prop, simply go along and coat the fibre generously with resin, if you have not:
Lightly brush the surface of your prop with resin, and then put a piece of the fibre onto it. Load up the brush and then generously apply resin to the fibre until it is saturated (it will go almost transparent).
Use the brush to push the fibre into corners, to get rid of bubbles or ripples, and to move it around until its where you want it. Once that’s done. Get the next piece of glass fibre and position it next to the one you just put down. Allow a small overlap (say 1 cm or so). Continue until you have coated all of the prop, filling in small gaps with smaller cuts of glass fibre.
If you are doing a single layer of fibreglass, look for areas that are going to take strain: near handles, resting surfaces, grip parts etc. reinforce these areas with another patch of fibreglass.
6. Allow to Cure
Allow to cure as you did with the resin coat. This may take longer as you have used a load more resin, so overnight is probably best. If you fibreglassed the inside of the prop, the outside will be dry and hard, so you can leave it to cure without worrying about damage.
7. Repeat Layers (if you want to)
If you are using multiple layers of fibreglass, its often better to wait for one layer to fully cure before adding the next – it also lets you see where you missed, or which areas might need more reinforcement. I would advise that if you are using multiple layers, the final layer should be fibre tissue, as it leaves a better finish, and hides away a lot of the mess.
Notes from the Field
- Pre-adhesion of the glass fibre material to the model using spray adhesive can save you time when the resin is mixed – less is more though- you don’t want to coat the surface with an impregnable layer of spray adhesive as it will reduce the new resin’s ability to get a good bond on the previous resin coat, weakening the new fibreglass layer’s bond to the model.
- You will get strands of glass fibre (especially if using chopped mat) all over the place. Do the cutting over a box lid or bin so that you wont need to sweep up – If you are messy with your resin, you’ll get fibres on your gloves which will transfer to brush handles – having a wet-wipe to hand will help sort this out but be sure to dispose of your contaminated brushes and pots before removing your gloves.
- The fibreglassing process can take a while – a resin coat may take 10 min, fibreglassing can take an hour or more depending on your prop, and how comfortable you are with the materials – accept the time span and don’t rush.
- If you missed a spot or feel that it could do with more reinforcement, you can come back later and add a second (or third) layer to specific parts.
OK, that was simple. We have just successfully polymer coated, cured, and then fibreglassed a prop. It should be pretty tough now, and noticeably heavier (but still, nowhere near as heavy as you’d think for its strength) –
For reference: the paper model was 60 g. The resin coated model was about 100g. The fibreglassed model was 370 g.
If your fibreglassing technique is not so tidy, you’ll need to clean up the edges:
I used a Dremel (rotary tool) with a cutting disk on it. Be sure to wear a long sleeved top, and a respirator in a well ventilated area when doing this – fibreglass dust is hazardous. You can reduce fibreglass dust to much lower levels using a coping saw or hack saw to clean it up (toothed tools go through resin and fibreglass much easier and with more control than my Dremel cutting disks). You might need to clean up the inside a bit too, to remove any glass fibres that didn’t set flush to the surface – on a final prop that is to be worn, we will be shaping the inside with padding which will reduce this problem.
Congratulations, you have now resin coated and fibreglassed a prop, using industry standard and professional quality materials.
We used polymer resins to give your prop a bit of strength, so that we can apply a heavier reinforcement (fibreglass) to it, and we went through the steps of how to apply it – you can use the same steps to repair items around the home (and outside – fibreglass & polymer resin ar water proof).
Hopefully you are now comfortable with the materials, and are ready to move onto body shaping and filling. But until then, grab yourself a cup of tea and give yourself 10 DIY man points.
Moving on to the final steps? Take a look at some of the handy tips and tricks (and problems) I have faced in the making of my own props here:
If you want a simpler build project, then I am also working on this (which is far simpler to follow along with):